Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6?

Question

[] 12 and 7
[] 12 and 8
[]120 and 70
[] 50 and 34

Answer 1

[] 12 and 7

Explanation:
Since the area of a triangle is given by 1/2 * base * height, if two triangles have the same area, the product of their base and height must be constant. So, if the first triangle has a base of 14 and a height of 6, the product of base and height is 14*6 = 84. For the second triangle, the base and height could be any pair of numbers whose product is also equal to 84. In this case, 12*7 = 84, so the possible base and height for the second triangle are 12 and 7.